Final answer:
To determine the proportions of hexane and heptane that should be mixed by mole fraction, you can use Raoult's law. The mole fraction of hexane can be calculated using the vapor pressure of hexane and heptane, as well as the total number of moles in the solution.
Step-by-step explanation:
To determine the proportions of hexane and heptane that should be mixed by mole fraction, we can use the information provided about the vapor pressures of pure hexane and pure heptane. The mole fraction of a component in a solution is equal to the ratio of its partial pressure to the total pressure of the solution.
Using Raoult's law, we can calculate the respective mole fractions of hexane and heptane. Let P1 be the vapor pressure of hexane, P2 be the vapor pressure of heptane, and X1 be the mole fraction of hexane.
Raoult's law states that P1 = X1 imes P total, where P total is the total pressure of the solution. Substituting the given values, we have 0.0562 atm = X1 imes (0.300 mol / 1 mol) + (0.700 mol / 1 mol).
Solving for X1, we can find the mole fraction of hexane in the solution. Similarly, the mole fraction of heptane is 1 - X1.